Together with the team, Havrysh became the second in his group of the Second League twice in a row (in 2004 and 2005), although only the winners of the groups rose in the class. In addition, in 2005 he was called up to the location of the national teams of Ukraine U-18 and U-19, but did not go on the field. Only on the third attempt, in 2006, Chernihiv managed to win their group and reach the First League.
In early 2007, Vitaliy moved to Donetsk "Metalurh", but was immediately leased to "Stal" from Alchevsk, which played in the Ukrainian Premier League and finished 15th that season and relegated to the First League. Vitaliy Havrysh started the next season in "Metalurh" Donetsk, but in a year the midfielder played only 2 matches in the championship and 2 in the cup (1 goal) for the main team, most of the time playing in the backup tournament (28 matches, 3 goals).
In the summer of 2008, Havrysh returned to "Stal", having played in 30 matches (4 goals) of the First League during the season, but after the end of the season he was returned to "Metalurh". But after playing only a few control matches and one backup match, in August of the same year he went to "Stal" again, where he became captain of the team.
On January 11, 2012, Havrysh returned to the Premier League, moving to "Olexandria". On March 3, 2012, he made his debut for Oleksandriya in a match against Lutsk's "Volyn". On April 8, 2012, he scored his first goal for "Olexandria" in a match against Kryvyi Rih's "Kryvbas", which won. Together with the club he flew from the Premier League to the First League, where he spent another six months.
On February 2, 2013 he moved to "Metalurh" from Zaporizhia. On March 2, 2013, he made his debut for "Metalurh" in a match against "Illichivets". In the game against the same team on December 7, 2014, Havrysh scored the first goal for the club.
In the summer of 2015, together with seven other players, he left "Metalurh" as a free agent.
On June 27, 2016, he became a "Zirka" player. But on September 29 of the same year he signed a contract with Kovalivka's "Kolos", where he later became a captain and remains so to this day.
Vitaliy Havrysh is the author of both goals in the return match of the playoffs of the 2018/2019 season against Odesa's "Chornomorets", in which "Kolos" defeated Odesa 2-0 at its stadium in Kovalivka. The first game in Odessa ended in a draw 0: 0. Thus, these goals of Havrysh brought Kovalivka club to the Ukrainian Premier League.
Havrysh is one of the guards of the Kovalivka club - players who have played more than 100 matches in the "Kolos" T-shirt.